Problem: Simplify the following expression: $a = \dfrac{-8n^2 + 16n + 192}{n + 4} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ a =\dfrac{-8(n^2 - 2n - 24)}{n + 4} $ Then we factor the remaining polynomial: $n^2 {-2}n {-24} $ ${4} {-6} = {-2}$ ${4} \times {-6} = {-24}$ $ (n + {4}) (n {-6}) $ This gives us a factored expression: $\dfrac{-8(n + {4}) (n {-6})}{n + 4}$ We can divide the numerator and denominator by $(n - 4)$ on condition that $n \neq -4$ Therefore $a = -8(n - 6); n \neq -4$